Regime Dependent Infection Propagation Fronts in an SIS Model

The paper proves front existence in three diffusion regimes using a conserved quantity to reduce dimension, Geometric Singular Perturbation Theory (Fenichel), and planar trapping-region arguments. It establishes: fronts for all c>0 in Cases 1 and 2, and a minimal-speed condition c ≥ 2√((β−(1+σ)γ)/(1+σ)) in Case 3. By contrast, the candidate’s argument fatally mis-reduces Case 3: it asserts S+I is constant on the ε=0 slow manifold and hence reduces the dynamics to a scalar KPP ODE I''+cI'+g(I)=0. The paper shows the correct slow manifold is S=1−I−V/c, so S+I is not constant and the reduced scalar equation has derivative-dependent nonlinearity (Burgers–FKPP when σ=0), not classical KPP. Although the candidate states the correct minimal speed, the proof step is invalid; Cases 1–2 are broadly consistent with the paper.